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Apr 27, 2019 at 20:02 vote accept M. Winter
Apr 25, 2019 at 19:19 comment added Ryan Budney Here is a little further discussion of the embedding Ben describes: ldtopology.wordpress.com/2012/07/12/…
Apr 25, 2019 at 13:47 history edited Ben McKay CC BY-SA 4.0
added more details on the metric and the subspace
Apr 25, 2019 at 9:29 comment added Vít Tuček You mean preserving the trace of the symmetric matrix, not $x^2 + y^2 + z^2$. (What are $x, y, z$ anyway?) The only detail left is for which scalar product $G$ on $\mathrm{Sym}^2 \mathbb{R}^3$ the conjugation by matrices from $\mathrm{O}(3)$ belongs to $\mathrm{O}(G)$.
Apr 25, 2019 at 8:10 history answered Ben McKay CC BY-SA 4.0